上海交通大学大学概率论与数理统计教学PPT12

1、Ch4-110 159711 1012 108810.1450cm 157101081091112810.145050505050cmCh4-3 850750155010501050128()10.14kDkP Xk (),1,2,kkP Xxpk1kkkx p 1()kkkE Xx p Ch4-5( )f x( )xf x dx ()( )E Xxf x dx 0()!kkE Xkek 1(1)!kkek 22()21()2xE Xxedx 2212xuuuedu 令令（） Ch4-711()(1)kkE Xkpp 111kkxppkx 11kkxppx 2111(1)xppxp Ch4-8

2、21( ),(1)f xxx 2|( )(1)xx f x dxdxx Ch4-9q (),1,2,iiP Xxpi1()iiig xp 1( )()iiiE Yg xp q ( )( ) ( )E Yg x f x dx ( ) ( )g x f x dx Ch4-10(,),1,2,ijijP Xx Yypi j,1()(,)ijiji jE Zg xyp ,1(,)ijiji jg xyp q ()( , ) ( , )E Zg x y f x y dxdy ( , ) ( , )g x y f x y dxdy Ch4-11()kE X(| )kEX() )kEXE X 2() )()

3、EXE XD XCh4-12()klE X Y () ( )klEXE XYE Y()E XY ()( )EXE XYE Y()( )()( )XYXE XYE YED XD Y Ch4-1322ZXY22()( , )E Zxy f x y dxdy2222212xyxyedxdy 2220012rrerdr d 2 1,20004000,2000( )0,Xxfx 其其它它3 ,()3() 1,yXyYg XXyXXy 3 ,( )4,yxyg xxyxy ( )( )( )XE Yg x fx dx 4000200011(4)320002000yyxydxydx261( 2140008

4、10 )2000yy( )1( 414000)2000dE Yydy0 令令22( )402000d E Ydy Ch4-17q 11()nniiiiiiEa XCa E XCq q Ch4-180()(1)nkkn knkE XkC pp 1!(1)!()!nkn kknkppknk 1(1) (1)1(1)!(1)(1)!()!nknkknnpppknk 1(1)10(1)nkknknknpCpp np 12,nXXX1,2,in ()iE Xp iX 1niiXX 1()()niiE XE Xnp Ch4-20(1)(0)1P XpP Xp()(1)0,1,2,kkn knP XkC p

5、pkn ()!0,1,2,keP Xkkk 1()(1)010,1,2,kP Xkpppk 1pCh4-211,( )0,axbf xba 其其它它2ab ,0,( )0,xexf x 其其它它1 22()21( )2xf xe Ch4-2221(13),02,01,( , )40,xyxyf x y 其其它它 ()( , )E Xxf x y dxdy 212001(13)4xxdxydy43 ( )( , )E Yyf x y dxdy 212001(13)4xdxyydy58 Ch4-23()() ( , )E XYxy f x y dxdy( , )( , )xf x y dxdyyf

6、 x y dxdy45473824()( )E XE YCh4-24()() ( , )E XYxy f x y dxdy 2120011(13)22xxdxyydy4 553 86()( )E XE YCh4-25( , )YyEf x y dxdyXx 2120011(13)22dxyydy58 Ch4-26 ()1()P XaP Xa1( )1F a( )0F a ( )0,F xxa()( )aE XxdF x ( )aadF x a Ch4-2744! 411243444C C P221344244()4CCC C 1444C81()64E X Ch4-281,0,iiX 第第 盒盒

7、空空，其其它它，1234XXXXX4314 43()4iE X 4381()4464E X 434Ch4-29125,XXX1,2,5min kkNX 51( )1(1( ),NkkFxFx 51,0,0,xex 其其它它，55,0,( )0,xNexfx 其其它它， 1()5E N 1,2,5max kkMX 51( )( )MkkFxFx 5(1) ,0,0,xex 其其它它，45(1) ,0,( )0,xxMeexfx 其其它它，()( )ME Mxfx dx 405(1)xxxeedx 13760 Ch4-31解解 1kp 11kp ()1(1)11kkiE Xpkp (1)1kkkp

8、 1()()1(1)11n kkkiinE XE Xpkpk Ch4-33思考思考 22(,) (),( , )1X YU DDx y xy(),( ),()E XE YE XY1,1020,10125,12XTXX 1 81 81 81 81 81 81 81 83 83 82 83 83 82 8Ch4-36 828284()( )0;E XE Y()0;E XY ()() ( )E XYE X E Y 1(1,1)8P XY 23(1) (1)8P XP Y Ch4-3722(,) (),( , )1X YU DDx y xy221,1,( , )0,xyf x y 其其它它22 1,11,( )0,Xxxfx 其其它它22 1,11,( )0,Yyyfy 其其它它( , )( )( )XYf x yfx fy Ch4-382112 1()0;xE Xx 2211()0;xyE XYxydxdy ()() ( )0E XYE X E YCh4-391,1020,10125,12XTXX Ch4-40(1)(10)(10)P TP X (20)(1012)(12)(10)P TPX (5)(12)1(12)P TP X ( )( 1) (10)